A Massively Parallel Reservoir Simulator

Abstract

Abstract A two-phase sequential IMPLICIT three dimensional reservoir simulator has been developed for massively parallel computer systems. The parallel algorithm is based on recently developed domain decomposition methods, The simulator has been tested using a 16384 processor MasPar MP-2. The simulator building blocks are robust Krylov space iterations using Additive Schwarz as the preconditioner. This approach naturally supports a distributed data structure with overlapping subdomains. In the simulator each subdomain is treated as a small reservoir in its own right, and each subdomain communicates with the neighbouring subdomains through boundary conditions. Previous work has shown that the use of minimal overlap is sufficient and computationally nearly optimal for these problems. To solve the pressure equation we use a two level Additive Schwarz preconditioner. The coarse grid problem is solved by a multigrid solver and each subdomain problem can be solved with a range of simple iterative or direct methods depending on time, space or robustness considerations. The saturation equation is solved by splitting the equation into one hyperbolic saturation equation and one elliptic saturation equation. The hyperbolic saturation equation is solved by the Modified Method of Characteristics. The solution of the (nonsymmetric) elliptic saturation equation is again obtained using an Additive Schwarz preconditioner. Introduction This paper describes and reports results obtained with a prototype of a new massively parallel black oil simulator. The main goal for the project has been to implement a numerical simulator on a Massively Parallel Computer. In commercial numerical reservoir simulators the finite difference method is the most commonly used discretisation technique, and the upstream weighting method is used to stabilise the convective flow problem. These methods introduce artificial numerical dispersion which are at the order of the grid size. On field-scale this limits the accuracy of the predicted flow pattern and the predicted hydrocarbon recovery. Techniques which control the numerical dispersion have had limited success in ordinary reservoir studies done by oil companies. The computing power of parallel computers now allows us to test and implement new numerical solution methods that greatly reduce numerical diffusion. The basic idea behind the parallelisation strategy is to exploit data locally by using a data structure where locally in the physical model implies locally in the computer representation. The domain decomposition approaches that we have followed, effectively separates short and long range communication into two distinct phases in each precondition step. It is then easier to analyze the performance of the method and to adjust the notion of locality with respect to the target computer at hand. Our goal is an algorithm that is portable and efficient in a distributed memory system. P. 467